Conditions are revealed and means are offered for minimizing burr formation at cutting of sheet material made of titanium alloy BT1-0 and steel 12X18H10T. The influence of imposing of mechanical vibrations in ultrasound range on burr formation was investigated and the possibility of reducing the amount of burr with ultrasonic influence was showed. The influence of wetting of a lower edge of molten metal on a cutting quality was investigated, the possibility of reducing the burr amount using coating was showed. The influence of pressure of an auxiliary gas on reducing the amount of burr was investigated and importance of this parameter was confirmed. The results allow 30-60 % reduction in the amount of burr under otherwise equal conditions.